What is a MIL?
A MIL is an angular unit which is derived by dividing a unit
circle into 6400 angles - very similar to how we divide a circle
into 360 degrees. The relation between MILS and degrees is as
follows, 6400 MILS = 360 degrees. This gives the MILS unit an
accuracy 17.777 times greater than a degree! So 1 degree =
17.777 MILS and 1 MIL = 0.05625 degrees.
How is a MIL derived?
The MIL unit is the angle formed by 1/1000 radians or put
another way, a MIL is one thousandth of a radian.
More generally, a MIL is the angle formed by a circle whose
radius is 1000m with an arc length of
1m.
Why use MILS instead of degrees?
The simple answer: Accuracy
When you project a waypoint over a long distance, an arc is
formed whose length is a function of both the projection angle and
the length of the projection.
Imagine you come to a cache waypoint which requires you to
project a waypoint 1000m away at an angle of 352 degrees true from
the waypoint you just found. If you use degrees, the length
of the arc that is formed is equal to 17.4m which means not only
does your GPSr have an error range that you have to consider when
searching, you have to search along a 17.4m long arc too! As
long as the arc length is smaller than your GPSr error at the
projected waypoint, you have very little to worry about.
If you use MILS, the length of the arc is only 0.98m long!
To equal the arc length of a 1000m projection using degrees, the
projected distance using MILS would have to be 17.7km long!
Therefore MILS are 17.7 times more accurate than degrees!
Not satisfied with the explanation? See the mathematical
answer below.
The mathematical answer: Less arc length = less
search area
Imagine that your current GPSr accuracy is 12m - which is quite
common under a forest canopy. This means that if you are
given a waypoint without having to project one (ie. no arc length
to worry about), your search area has a 12m radius which gives you
a total search area of 452m². Recall that the area of a circle is
p * r².
This seems like a large search area, but what happens when
you have to search an arc?
Using the example from the simple explanation (above), if a
projected waypoint 1000m away was done using degrees, the arc
length we have to search is 17.4m long. How is this
calculated?
arc length = (radius * p * degrees) / 180
where the projected
distance is the radius, and degrees = 1 (because this is the error
range of a single bearing)
So now we have an arc length to
deal with in terms of search area - no problem, we will
approximate the length of the arc to being a straight line for
ease of calculation. In reality, calculus would be
required to calculate the exact area.
search area = (p * r²) +
(2 * r * arc length)
This simplistic equation calculates the area of a circle using
the GPSr accuracy as a radius and then calculates the area of a box
whose length is equal to the arc length and whose height is twice
the radius of the circle.
Using the exact data from above, with an arc length of 17.4m and
a GPSr error of 12m, the entire search area for our projected
waypoint is a whopping 870m²! This is a relatively large search area!
So what about the search
area for a waypoint projection of 1000m using MILS? The
search area is a mere 475m² which is almost half the area to
search!
As a tip, a "hasty calc"
for the arc length can be done using the tan function of your
calculator. The longer the projection, the less
precise this method becomes, however it is much less cumbersome
than the full arc length equation.
Simply
use:
- length = projected
distance * tan(1) for degrees
- length = projected
distance * tan(0.05625) for
MILS
Ok, so now you should
better understand what MILS are and why it is better to use MILS
when projecting a waypoint! In this exercise, the first few
waypoints will be set in such a way that you can calculate the next
waypoints before heading out, however, the other waypoints you will
encounter will only provide you with the required data when you
arrive in the field!
WP1 = N45 aa.bbb W075
cc.ddd
Using what you know of
MILS, calculate the number of mils in 1.6409 degrees.
Take your result to be in the form aa.bbb by rounding to the third
decimal place.
Now calculate the number of degrees in 531.857
MILS. Take your result to be in the form cc.ddd by
rounding to the third decimal place.
WP1 = N45 ___._____ W075
___._____
WP2 = N45 ee.fff W075 gg.hhh
Calculate the arc length of a projection using degrees
given a distance of 1.6751 km. Take your result to be in the
form ee.fff by rounding to the third decimal place.
Calculate the arc length of a projection using MILS given
a distance of 30.3499 km. Take your result be in the form
gg.hhh by rounding to the third decimal place.
WP2 = N45 ___._____ W075
___._____
Now that you have the first two waypoints figured out, it is
time to find both waypoints to collect the data you will find
there.
To find the final cache location, you will need the distance and
the bearing to project a new waypoint!
- You can find the bearing in MILS from WP2 to the cache
location on a brass tag at waypoint 1.
- This tag will have the form: xxxx MILS
- You can find the distance from WP2 to the cache on a
brass tag at waypoint 2.
- The tag will have the form: xxxx m
WP3 = ____________ m at ___________ MILS
from waypoint 2.
Once you have both pieces of information (distance and bearing),
you can project a waypoint on your GPSr. Remember to go into
the GPSr setup menu and change the bearing units to MILS for this
exercise + be sure that your GPSr is set to True North!
For those who have a Garmin eTrex, you can perform the required
setup changes as follows:
to change your bearing to MILS: main menu > setup >
heading > display > mils
to change your north reference: main menu > setup >
heading > north reference > true
To project a waypoint on a Garmin eTrex, do the following when
standing at WP2:
find waypoint > nearest > select WP2
When you are at the data screen that shows the waypoint
information, select the little "text box" (where the red arrow is
pointing) in the upper right corner (not the X !) and then select
"project waypoint". Once in the waypoint projection screen,
give the new waypoint a meaningful name such as MILSCACHE and
change the symbol to Geocache. Once the name and icon are
sorted out, enter in the distance that you got from WP1 and then
enter in the bearing (in MILS) that you got from WP2.